Business Calc: total cost (7/8)x^2+5x+1, price 15-(3/8)x,...

[geekie]

I've no idea is it the right section to post this,
But I had some problems dealing with this problem.

Total costs

Market price

Tax (per unit produced)

Find:
1. Quantity to produce to maximise profits
2. What should t be, so as to maximise tax revenue?

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What I've done:

I derived the profit function as:

Then, I differentiate the profit function:

Then I'm stuck cos' I can't find x.

 

[stapel]

For any unable to view the pictures of the text, the exercise is as follows:

Total costs
\(\displaystyle \frac{7}{8}x^2\, +\, 5x\, + 1\)

Market price
\(\displaystyle 15\, -\, \frac{3}{8}x\)

Tax
\(\displaystyle t\)

Find
Quantity to produce to maximize profits
What should t be, so as to maximize tax revenue?